Its not that bad..
"add games that aren't sold by steam" could mean one of two things.
a. I bought a steam code from somewhere other than steam, and would like to add it to my Steam Entitlement Library
b. I bought a retail version of the game (boxed version, or digital download from Uplay, Origin) and want to add it to my Steam Entitlement.
If a., once you plug in the code into Steam, the game will activate just like you bought it from the Steam Store.
If b., things can get trickier as discussed above.
Good news is 95% of what most people want to play is already on steam, so its not a big deal.
As mentioned, most of the games on Humble Bundle are steam codes. Games that "unlock" via steam will have the steam logo on them. Going Home has this logo so your experience would look like this.. Sign up for steam account, sign up for humble bundle, register steam account (on HB), buy game, click "activate on steam". From there, it appears in your library (Steam) ~ click to DL and play just like Smogs said.
Other stores also sell these "steam codes", Amazon, Gamefly, Greenman, etc and they always work the same way... Get a key, plug it into steam and they are attached to your account indefinitely. You just need to make sure they have the steam logo, or "steamworks" DRM and you're good.